線性代數

臺北科技大學 115-1 學期課程，課號 363139。

課程大綱

線性代數為工程類學科之基礎數學之一，著重於訓練學生矩陣運算及基本數學証明。課程大綱如下： 1. 解聯立方程式 2. 矩陣運算 3. 行列式 4. 向量空間 5. 線性轉換 6. 特徵值及特徵向量 7. 選擇性題材，視時間充許教授下列之一：矩陣數值方法，Jordan form或線性規劃 As a basic mathematics in engineering, the course Linear Algebra emphasizes on the subject of matrix computation (theory) and the technique of mathematical proving. The outline of the course includes the following: 1. Systems of Linear Equations 2. Matrices 3. Determinants 4. Vector Spaces 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Advanced Topics: select one of the following if time permitted: Numerical Techniques in Matrix operations, Jordan form, or Linear Programming.

課程進度

Week 1 - Week 2 1. Matrix Operations (Sections 2.1 and 2.2) To learn basic matrix arithmetic operations: addition, subtraction, multiplication power, transpose, and inverse. Week 3 - Week 5 2. Linear Equations (Sections 1.1 to 1.5) To understand the basic terminologies and notations of matrices and systems of linear equations, in the forms of vector equation and matrix equation. Solving a system of linear equations by reducing a matrix to its echelon form. Week 6 - Week 7 3. Introduction to Linear Independence and Linear Transformation (Sections 1.7, 1.8, and 2.3) First exposure to key concepts such as linear independence and linear transformation. More about the matrix inverse. To summarize the concepts for systems of n linear equations in n unknowns. Week 8 Midterm Exam Week 9 - Week 11 4. Vector Spaces (Chapter 4) Introduction to vector spaces. Fundamental subspaces of a matrix: column space, row space, and null space. Basis and dimension of a vector space. Week 12 - Week 13 5. Eigenvalues and Eigenvectors (Chapter 5) To understand the meaning of eigenvalues and eigenvectors of a matrix, and the approaches to find them. Diagonalization of a matrix (linear transformation). Week 14 - Week 15 6. Orthogonality and Least Squares (Chapter 6) To introduce inner product of vectors, and thus the geometric concepts of length, distance, and angle (perpendicularity). To be familiar with the use of orthogonal bases. Least-Squares approximation. Week 16 Final Exam Week 17 - Week 18 Flexible Learning

評量方式

1. In-class attendance, Zuvio IRS practice and TA class attendance (上課點名/問答), at most 5%. 此為加分項目(點名都到不一定加到滿分) 2. Written exercises (課本練習題、紙筆類型), 15%. Hand in your homework before class. The lowest score will be discarded. 3. In-class quizzes (隨堂考), 20%. 第二次以後請假成績以零分計算。 The grade of the quiz since the second absence on leave will be zero. 4. Two 50-minute tests (段考), 10% each. (20%) 5. Midterm exam (期中考), 20%. 6. Final exam (期末考), 25%.

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 David. C. Lay, Stephen R. Lay, and Judy J. McDonald, Linear Algebra and its Applications, Sixth Edition, Pearson Education Limited, 2022.（偉明書局代理）